Pet's Hands

Pet's hands are made to look like Bitter's hands, which immediately stand out to Jam, and these symbolize Pet's humanity. While he is not human, there are human elements of the creature, and the hands are the human part that Jam notices.

The Canvas

Bitter paints Pet on a canvas, and the canvas is a symbolic door through which Bitter manifests her feelings and talent. The canvas also turns out to be a literal door between realms, and Pet passes through it. In an interesting twist, Bitter uses chips of razor blades in the painting and those do not remain part of Pet because they are not paint.

Pet's Name

Pet tells Jam his name, and the name is meant to be an ironic symbol of the fact that he is present in Lucille to hunt monsters. Pet looks very much like a monster himself...